Finite-element analysis of a static fluid–solid interaction problem

Rodolfa Araya, Gabriel Barrenechea, Fabrice Jaillet, Rodolfo Rodriguez

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Abstract

This paper deals with a fluid–solid interaction problem inspired by a biomechanical brain model. The problem consists of determining the response to prescribed static forces of an elastic solid containing a barotropic and inviscid fluid at rest. The solid is described by means of displacement variables, whereas displacement potential and pressure are used for the fluid. This approach leads to a well-posed symmetric mixed problem, which is discretized by standard Lagrangian finite elements of arbitrary order for all the variables. Optimal-order error estimates in the H1- and L2-norms are proved for this method. A residual a posteriori error estimator is also proposed, for which efficiency and reliability estimates are proved. Finally, some numerical tests are reported to assess the performance of the method and that of an adaptive scheme based on the error estimator.
Original languageEnglish
Pages (from-to)886-913
Number of pages28
JournalIMA Journal of Numerical Analysis
Volume31
Issue number3
Early online date9 Apr 2010
DOIs
Publication statusPublished - 2011

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Keywords

  • fluid–solid interaction
  • adaptive scheme
  • a priori and a posteriori error estimates
  • finite elements
  • biomechanical brain model

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